An investigation of the effects of using a new treatment of chronic lymphocytic leukemia and indolent Non-Hodgkin's lymphoma. A combination of Bryostatin 1, an experimental drug, and fludarabine, an established drug, will be given to 35 patients. The purpose of the study is to determine the safety, side effects, and correct doses of the combination in patients with symptomatic or advanced chronic lymphocytic leukemia (CLL) and relapsed, indolent (Non-Hodgkin's) lymphoma according to two sequences of administration. Also, to monitor apoptosis (fragmentation of a cell into membrane bound particles), differentiation, and a protein kinase C activity in leukemic lymphocytes exposed in vivo to bryostatin and fludarabine. And, to observe the anti-tumor activity of the combination of drugs in patients with CCL and relapse indolent lymphoma. Patients who have CCL or a previously treated lymphoma will receive fludarabine daily for five days and bryostatin for one day just before or after the fludarabine treatment. Order of the administration of the two drugs will be randomly determined and the doses will be measured by the experience of the patients previously treated. Dose increase will stop when serious side effects appear. Both drugs will be administered intravenously. Bryostatin will be continuously infused for 24 hours. Fludarabine will be infused for 30 minutes for five consecutive days. The treatment will be repeated every four weeks as long as the leukemia/lymphoma shrinks or remains stable and the side effects are acceptable. Progress will be checked during treatment by blood tests, physical exams, and other tests. Several extra blood samples will be used to determine how the drugs are acting in the body.